Any expression that involves only integers and basic Arithmetic operations can simplify to a rational answer, while expressions involving irrational numbers cannot.
There are several expressions that simplify to a rational answer. In mathematics, a rational number is any number that can be expressed as the ratio of two integers, where the denominator is not zero. Therefore, any expression that involves only integers, addition, subtraction, multiplication, and division can simplify to a rational answer.
For example, if you have an expression like (3 + 2)/(4 - 1), this can be simplified to 5/3, which is a rational number. Similarly, expressions like 6/3 or 7 - 2 also simplify to rational answers.
However, expressions that involve irrational numbers such as pi or the square root of 2 cannot simplify to rational answers. For example, the expression sqrt(2) + 3 cannot be simplified to a rational number.
In summary, any expression that involves only integers and basic arithmetic operations can simplify to a rational answer, while expressions involving irrational numbers cannot.
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How would you solve this?
Answer:
average rate of change = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
the average rate of change of h(x) in the interval a ≤ x ≤ b , is
[tex]\frac{h(b)-h(a)}{b-a}[/tex]
here the interval is - 2 ≤ x ≤ 2 , then
h(b) = f(2) = [tex]\frac{1}{8}[/tex] (2)³ - 2² = [tex]\frac{1}{8}[/tex] (8) - 4 = 1 - 4 = - 3
h(a) = h(- 2) = [tex]\frac{1}{8}[/tex] (- 2)³ - (- 2)² = [tex]\frac{1}{8}[/tex] (- 8) - 4 = - 1 - 4 = - 5
then average rate of change
= [tex]\frac{-3-(-5)}{2-(-2)}[/tex]
= [tex]\frac{-3+5}{2+2}[/tex]
= [tex]\frac{2}{4}[/tex]
= [tex]\frac{1}{2}[/tex]
A basketball team won a game by 22 points and then beat the same team by 12 points in a re-match. The total score of the winning team across both games was 190 points. What was the total score of the team that lost?
You plan to save $5000 in an account which pays 4.5% interest compounded monthly.
How much money will you have at the end of 3 years? Use your FORMULA from your notes.
Make sure to LABEL each variable. You must show your work.
We can use the formula for compound interest to calculate the amount of money we will have at the end of 3 years:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money we will have at the end of 3 years
P = the principal (the initial amount we start with)
r = the interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
Plugging in the given values, we get:
A = 5000(1 + 0.045/12)^(12×3)
A = 5000(1.00375)^36
A ≈ $5,622.16
Therefore, we will have approximately $5,622.16 at the end of 3 years.
On a 6 question multiple-choice test, where each question has 5 answers, what would be the probability of getting at least one question wrong?
Answer:
[tex]\frac{24}{5}[/tex]
Step-by-step explanation:
We Know
The test has 6 questions.
Each question has 5 answers.
What would be the probability of getting at least one question wrong?
Each question can only have one correct answer, so the probability of getting a wrong answer for each question is [tex]\frac{4}{5}[/tex]
There are 6 questions on the test, so we take
[tex]\frac{4}{5}[/tex] x 6 = [tex]\frac{24}{5}[/tex]
So, the probability of getting at least one question wrong is [tex]\frac{24}{5}[/tex]
0.85 divided by 3 2/5 divided by 3/4
Answer: 1/3
Step-by-step explanation: To do complex equations like this try using a calculator
Question 8 of 10
Find the total price of the three items in the chart below. Enter your answer in
the space provided. Do not include $ in your answer.
ITEM
Bagels
Cream Cheese
Raisins
Answer here
COST
$2.17
$2.82
$3.74
Answer:
$8.73 --> 8.73
Step-by-step explanation:
We need to add their costs together to find the total price of the three items.
The cost of Bagels is given as $2.17.
The cost of Cream Cheese is given as $2.82.
The cost of Raisins is given as $3.74.
Adding these three costs together gives us:
$2.17 + $2.82 + $3.74 = $8.73
Therefore, the total price of the three items is $8.73.
If a = 4, then a³ + a=
I know the answer but can someone explain step by step
Make a new triangle
B
15
Ch
17
8
The Finale! All trig ratios for a right triangles
Complete the table below using what you know about
trigonometric ratios for right triangles.
LA
Write your ratios as fractions. A message will appear
when you are correct.
angle
LB
opp
adj
hyp
sin
COS
8
17
15
17
tan
15
8
15
8
Angle A is the right angle, so the trigonometric ratio we get is sin(LA) = 8/17, cos(LA) = 15/17, tan(LA) = 8/15, sin(LB) = 15/17, cos(LB) = 8/17, tan(LB) = 15/8
What is the trigonometric ratio?Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios. (sec). A branch of mathematics called trigonometry in geometry works with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.
The right triangle with sides that are 8, 15, and 17 in length needs to be labeled as follows in order to use trigonometry ratios.
B
/|
17/ |
/ |
/___|__
A C 15
where the right angle A is. The chart can then be filled out as follows:
angle opp adj hyp sin cos tan
LA 8 15 17 8/17 15/17 8/15
LB 15 8 17 15/17 8/17 15/8
The tangent is opposite/adjacent, the sine is adjacent/hypotenuse, and the cosine is opposite/hypotenuse.
The trigonometry ratios for the right triangle with sides that are 8, 15, and 17 in length are as follows.
sin(LA) = 8/17
cos(LA) = 15/17
tan(LA) = 8/15
sin(LB) = 15/17
cos(LB) = 8/17
tan(LB) = 15/8
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Parallelogram DEFG is transformed to parallelogram VSTU.
Parallelogram D E F G is reflected diagonally to form parallelogram V S T U.
The True statement is parallelogram DEFG is the pre-image because it is not the result of the transformation.
What is Transformation?
A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
Given:
Parallelogram DEFG is transformed to parallelogram VSTU.
It changes from parallelogram DEFG to parallelogram VSTU.
According to how it is said, DFEG is the initial parallelogram or pre-image that is changed to create VSTU, VSTU is changed from DEFG.
The following is an accurate statement concerning the transformation:
As the parallelogram DEFG is not the outcome of the transformation, it is the pre-image.
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The correct Question attached here are as follow:
(Q). Parallelogram DEFG is transformed to parallelogram VSTU. Which statement about the transformation is true?
Parallelogram DEFG is the pre-image because it is not the result of the transformation.Parallelogram DEFG is the image because it is the result of the transformation.Parallelogram VSTU is the pre-image because it is the result of the transformation.Parallelogram VSTU is the image because it is not the result of the transformation.On December 4, 2016, Dan Johnson, delivery truck driver for Farmers Products Inc., ran a stop sign and collided with another vehicle. On January 8, 2017, the driver of the other vehicle filed suit against Farmers Products for damages to the vehicle. Estimated damages to this vehicle were between $6,000 and $10,000 with no amount within the range more likely than any other amount. Farmers Products issued its 2016 financial statements on March 3, 2017.
Farmers Products Inc. should disclose a contingent liability in its 2016 financial statements for the lawsuit filed against them due to a collision caused by one of their delivery truck drivers.
Based on the information provided, it appears that as of the date of the financial statements (March 3, 2017), Farmers Products would need to disclose a contingent liability related to the lawsuit filed against them by the other driver.
A contingent liability is a potential liability that may arise from past events but the outcome is uncertain and will depend on future events. In this case, the lawsuit filed against Farmers Products by the other driver represents a potential liability that may result in damages being awarded against the company.
Under accounting standards, a contingent liability should be disclosed in the notes to the financial statements if it is probable that a liability has been incurred and the amount of the liability can be reasonably estimated. In this case, it is probable that Farmers Products may be liable for damages resulting from the accident and the estimated damages fall within a reasonable range of $6,000 to $10,000.
Therefore, in the notes to its 2016 financial statements, Farmers Products should disclose the existence of the lawsuit and the potential liability that may result. The disclosure should also include an estimate of the potential damages, if any, and any other relevant information about the lawsuit.
The question is incomplete; please see below for the whole question -
On December 4, 2016, Dan Johnson, a Farmers Products Inc. delivery truck driver, ran a stop sign and collided with another vehicle. On January 8, 2017, the driver of the other car filed a lawsuit against Farmers Products for vehicle damages. Damage to this vehicle was estimated to be between $6,000 and $10,000, with no value within that range being more likely than any other. Farmers Products' 2016 financial statements were released on March 3, 2017.
1. Prepare the disclosures and/or journal entries that Farmers Products should include in its financial statements for the fiscal year ending December 31, 2016.2. How would the disclosures and/or journal entries alter if Farmers Products employed IFRS versus US GAAP?
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Learning Task 2 : Find the area of each shaded region. Assume that all angles that appear to be right triangle (3 points each).
Thus the shaded area of the given rectangular figure is found as : 60 sq. ft.
Define about the rectangular figure:It needs four sides.There are two pairs of congruent sides on the four sides. This implies that the length of the sides that are opposite one another must be the same.Equal diagonal lengths are necessary. A diagonal line formed by joining two opposing vertices is equal to another diagonal line also formed. They absolutely meet in the midway of the other.Area of rectangle = length x width
Complete rectangular area = 12 ft x 7 ft
Complete rectangular area = 84 sq. ft.
Inner rectangular area = 8 ft x 3ft
Inner rectangular area = 24 sq. ft
Shaded area = Complete rectangular area - Inner rectangular area
Shaded area = 84 sq. ft. - 24 sq. ft
Shaded area = 60 sq. ft
Thus the shaded area of the given rectangular figure is found as : 60 sq. ft.
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Complete question:
find the shaded area of the given rectangular figure.
URGENT PLEASEEE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Neil is creating a computer game in which bubbles represented by circles collide, merge, and separate in different ways. A bubble with a radius of 8 centimeters separates into small bubbles, each of which has a radius of 2 centimeters. The area of the large bubble is equal to the sum of the areas of the small bubbles. How many small bubbles are there?
There will be 16 small circular bubbles.
What is circle?A circle is a shape formed by all points in a plane that are at a particular distance from the centre. It is the curve sketched out by a point moving in a plane so that its distance from a given point remains constant. The radius is the distance between any two points on a circle and the centre.
The area of a circle is given by the formula A = πr², where A is the area and r is the radius.
The area of the large bubble is A = π(8cm)² = 64π cm².
The area of a small bubble is A = π(2cm)² = 4π cm².
Let's assume that the number of small bubbles is n. Then, the total area of the small bubbles is n times the area of a single small bubble:
n(4π) = 4nπ cm²
According to the problem, the area of the large bubble is equal to the sum of the areas of the small bubbles:
64π = 4nπ
Dividing both sides by 4π, we get:
n = 16
Therefore, there are 16 small bubbles.
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There are 200 members in a club. 60% of them are males. How many percent more males than females are there?
Answer: If 60% of the members are males, then 40% of the members are females. We can calculate the number of males and females as follows:
Number of males = 60% of 200 = 0.6 * 200 = 120
Number of females = 40% of 200 = 0.4 * 200 = 80
To find out how many percent more males there are than females, we can use the following formula:
% more males = (number of males - number of females) / number of females * 100%
Substituting the values we found, we get:
% more males = (120 - 80) / 80 * 100% = 50%
Therefore, there are 50% more males than females in the club.
Step-by-step explanation:
Terrell wants to take group fitness classes at a nearby gym, but needs to start by selecting a membership plan. With the first membership plan, Terrell can pay $30 per month, plus $1 for each group class he attends. Alternately, he can get the second membership plan and pay $15 per month plus $4 per class. If Terrell attends a certain number of classes in a month, the two membership plans end up costing the same total amount. How many classes per month is that? What is that total amount?
Let's assume that Terrell attends x number of classes in a month. Then, the total cost of the first membership plan would be:
Cost of the first membership plan = $30 + $1 * x
Similarly, the total cost of the second membership plan would be:
Cost of the second membership plan = $15 + $4 * x
As per the problem statement, both membership plans cost the same when Terrell attends a certain number of classes in a month. So, we can equate the above two expressions and solve for x:
$30 + $1 * x = $15 + $4 * x
$2 * x = $15
x = 7.5
Since the number of classes cannot be a fraction, we can round up to the nearest integer, which is 8. Therefore, Terrell needs to attend 8 classes per month to make both membership plans cost the same.
To find the total amount, we can substitute x = 8 in either of the above expressions:
Total amount = $30 + $1 * 8 = $38
Therefore, Terrell needs to attend 8 classes per month, and the total amount would be $38.
(6.EE.5) Select the equation where x=3
is a solution.
Answer: x-3=0
Step-by-step explanation: With the equation it is basic algebra. So right now the equation is x-3=0. You will go plus 3, plus 3 on both sides. That would get rid of your negative 3 and make your 0, 3. So what you should have left is, x=3.
use the points (6,56) and (12,26) from the following data set to determine the point-slope form of an equation that represents the data set. x 5 6 7 8 10 11 12 12 14 y 58 56 53 46 37 33 26 23 13 answer
The point-slope form of the equation that represents the data set is y - 56 = -5(x - 6), or y = -5x + 86.
EquationsWe are given two points: (6,56) and (12,26) from the data set. We can use the point-slope form of a linear equation to find an equation that represents the data set.
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope of the line.
To find the slope, we use the two given points:
m = (y2 - y1) / (x2 - x1)
m = (26 - 56) / (12 - 6)
m = -30 / 6
m = -5
Now that we have the slope, we can use one of the given points, say (6, 56), to write the point-slope equation:
y - y1 = m(x - x1)
y - 56 = -5(x - 6)
y - 56 = -5x + 30
y = -5x + 86
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3.9+3.4+4.5+3.1+3.9+4.1+3.6+3.9
Answer: 30.4
Step-by-step explanation:
Every day, people face problems at home, work, school, or in their community that they must solve. Think about your life from the past 2 weeks, when something did not work out the way you intended, such as your car breaking down, you running out of milk, or facing a scheduling conflict. A lot of them need you to use math to help solve the problem.
Share at least 1 problem that you encountered recently, and answer the following questions in your main post:
What was the problem, and why it was difficult for you?
How did you use math in trying to solve the problem, and what was the outcome?
How would you approach in the problem differently next time?
personal experience based .
why we use mathematics in daily life ?maths gives us a way to understanding patterns ,define relationships , and predict the future.
One of my friends wanted to host a dinner party at her house, and she asked me to help her plan the menu. She told me that she was expecting around 10 guests, and she wanted to make sure that she had enough food for everyone. The difficult part was that she had a limited budget and wanted to keep the cost of ingredients low.
Mathematical approach:
To help my friend plan the menu, I used math to estimate the amount of food we needed to buy. I researched online to find the average portion sizes for the dishes we were planning to serve and calculated the total amount of ingredients needed based on the number of guests. Then, I compared the cost of the ingredients at different grocery stores to find the best deals and estimated the total cost of the meal.
Outcome:
By using math, we were able to plan a menu that was within my friend's budget and had enough food for all the guests. We were also able to find the best deals on ingredients, which helped us save money.
Approach for next time:
Next time, I would try to involve my friend more in the mathematical calculations to make sure she understands how to plan a meal within her budget. I would also consider making a list of alternative dishes that we could serve in case we were unable to find a certain ingredient or if it was too expensive.
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Select the correct answer from each drop-down menu.
Brian and Leo are flying to their grandmother's house on an airplane where 50 out of the 150 seats are window seats and passengers are randomly
assigned seats on the plane for each flight.
which is
the probability that Brian is assigned a window seat on the flight to his grandmother's house and the flight home from his
The probability that both Brian and Leo are both assigned window seats on the way to their grandmother's house is
grandmother's house.
The probabilities of Brian and leo being assigned a window seat on each flight are 1/9
what is the probability that Brian is assigned?The probability that Brian is assigned a window seat on the flight to his grandmother's house is:
50/150 = 1/3
The probability that LEO is assigned a window seat on the flight home from his grandmother's house is also:
50 window seats/ 150 seats = 1/3
The probability that both Brian and Leo are both assigned window seats on the way to their grandmother's house is:
50 window seats/150 seats * 49 window seats/ 149 seats = 1/9
Take note that Brian and Leo's chances of getting a window seat on each flight are independent, so we can simply multiply the odds to determine the likelihood of both happening.
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A chess player won 3 out of 4 games, or 75% of her games, during a tournament. Her goal this season is to win 90% of the
tournament games she plays.
How many more consecutive tournament games would she need to win to meet her goal?
Answer:
She needs to win 6 more consecutive tournament games.
Step-by-step explanation:
[tex] \frac{3 + x}{4 + x} = \frac{9}{10} [/tex]
[tex]10(3 + x) = 9(4 + x)[/tex]
[tex]30 + 10x = 36 + 9x[/tex]
[tex]x = 6[/tex]
Find the greatest common factor of 3, 15, and 35.
the gcf of 3, 15, and 35 is 1.
Answer: 1
Step-by-step explanation:
GCF means greatest common factor.
And the greatest common factor of 3, 15 and 35 would be 1 since
no other number is common between them.
3 * 1 = 3
15 * 1 = 15
35 * 1 =35
Determine the radius or diameter based upon the given dimensions. d = 20 cm
For the given diameter d=20 cm, the radius is 10 cm.
What is radius?
Radius is a straight line segment that connects the center of a circle or sphere to any point on its circumference or surface respectively. It is a fundamental measurement used in geometry and is denoted by the letter "r". The radius is half the diameter of a circle or sphere, and it is used to calculate important properties of the circle or sphere, such as its circumference, area, and volume.
If d = 20 cm, then d represents the diameter of a circle.
To find the radius (r) of the circle, we divide the diameter by 2:
r = d/2 = 20 cm/2 = 10 cm
Therefore, for diameter d=20 cm, the radius of the circle is 10 cm.
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Algebra-Which factor makes these equations correct?? 6xk=54 Kx9=81
Answer:9
Step-by-step explanation: it’s nine because 6×9 = 54
-2/3w=12 solve for w
help ASAP
Using a standard deck of cards, a gamer drew one card and recorded its value. They continued this for a total of 100 draws. The table shows the frequency of each card drawn.
Card A 2 3 4 5 6 7 8 9 10 J Q K
Frequency 4 7 5 6 7 6 8 10 7 10 8 12 10
Based on the table, what is the experimental probability that the card selected was a K or 6?
one over 26
four over 25
one fourth
8 over 13
The experimental probability that the card selected was a K or 6 is [tex]3/20[/tex].
The answer is "three over twenty."
What is probability?The frequency of K and 6 in the table are 8 and 7 respectively. Therefore, the total number of times a K or 6 was drawn is [tex]8 + 7 = 15[/tex].
The total number of draws was 100, so the probability of drawing a K or 6 on any one draw is:
Probability of K or 6 =[tex](Frequency of K + Frequency of 6) / Total number of draws[/tex]
[tex]= (8 + 7) / 100\\= 15 / 100\\= 3 / 20[/tex]
So the experimental probability that the card selected was a K or 6 is [tex]3/20[/tex].
Therefore, the answer is "three over twenty."
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8TH GRADE MATH HELP 30 POINTS
Thus, equation of line in slope intercept form: y = 5x + 3.
Define about the slope intercept form:One approach to calculating the equation of a straight line is the slope-intercept form. The two point form, point-slope form, plus intercept form are the further approaches.
The equation of a straight line is expressed using an equation in the slope-intercept form.You must determine the line's slope and the equation's y intercept form in order to get the slope-intercept form. The slope is a measurement of how steep a line is.Passing points - (-2, -7)
slope m = 5
The standard slope intercept form for equation of line:
y = mx + c
m is the slope and c is the y-intercept.
Put the given values and find c.
-7 = 5(-2) + c
c = -7 + 10
c = 3
Thus, equation of line in slope intercept form:
y = 5x + 3
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If the measure of A equals 61°, what is the measure of B?
If the measure of m∠A = 61°, the angle measure m∠B = 29°.
What is an angle?
Since ΔABC is a right-angled triangle with C as the right angle, we can use the trigonometric ratios to find the missing side lengths and angles.
Given that A = 61°, we know that m∠B = 180° - 90° - 61° = 29° (by the angle sum property of a triangle).
Now, we can use the trigonometric ratios to find the side lengths. Let's start with side AC = x.
From the definition of the sine ratio, we have:
sin(A) = opposite/hypotenuse
sin(61°) = z/x
Therefore, we have:
x = z/sin(61°)
Similarly, from the definition of the cosine ratio, we have:
cos(A) = adjacent/hypotenuse
cos(61°) = y/x
Therefore, we have:
x = y/cos(61°)
Since both expressions equal x, we can set them equal to each other and solve for z:
z/sin(61°) = y/cos(61°)
z = y*tan(61°)
Finally, we can use the Pythagorean theorem to find the length of side BC:
y² = x² - z²
y² = (y/cos(61°))² - (y*tan(61°))²
Simplifying, we get:
y = x*cos(61°)
So, the lengths of the sides are:
AC = x = z/sin(61°)
BC = y = x*cos(61°)
And the missing angle is:
B = 29°
What is trigonometric ratio?
In mathematics, a trigonometric ratio is a ratio of the lengths of two sides in a right-angled triangle. The three primary trigonometric ratios are:
Sine (sin) = Opposite / Hypotenuse
Cosine (cos) = Adjacent / Hypotenuse
Tangent (tan) = Opposite / Adjacent
In these ratios, the hypotenuse is the longest side of the triangle, and it is always opposite to the right angle. The opposite side is the side opposite to the angle of interest, and the adjacent side is the side that is adjacent to the angle of interest (but not the hypotenuse).
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Complete question is: If the measure of m∠A = 61°, the angle measure m∠B = 29°.
Which expression is equivalent to 3(−2.4y − 16.5)?
0.6y − 16.5
0.6y − 13.5
−7.2y − 16.5
−7.2y − 49.5
I picked b please tell me why im wrong i am stuck
Answer:
D. -7.2y - 49.5 is the correct answer.
Step-by-step explanation:
Distributing the 3 to the terms inside the parenthesis, we get:
3(-2.4y - 16.5) = -7.2y - 49.5
-2.4 x 3 = -7.2
16.5 x 3 = 49.5
so the expression that is equivalent to 3(-2.4y - 16.5) is -7.2y - 49.5
hope this helps
A sample of students is taken from the school's A honor roll. The school estimates that there are actually 360 students on the A honor roll. Using this sample from the table, how many students on the A honor roll are 8th graders?
280 8th graders
172 8th graders
114 8th graders
126 8th graders
The estimated number of students on the A honor roll who are 8th graders is 126.
What is Algebra?Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols. It involves using letters and other symbols to represent numbers and quantities in equations and formulas.
The main goal of algebra is to find the value of an unknown quantity, called a variable, by using known quantities and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions can be solved using various techniques, including simplification, factoring, and solving equations.
The total number of students on the A honor roll is given by adding the number of students in each grade:
Total = 15 (6th grade) + 11 (7th grade) + 14 (8th grade) = 40
To find the proportion of students who are in 8th grade, we can divide the number of 8th graders by the total number of students:
Proportion of 8th graders = 14/40 = 0.35
To estimate the number of students on the A honor roll who are 8th graders, we can multiply the proportion of 8th graders by the total number of students on the A honor roll:
Estimated number of 8th graders = 0.35 x 360 = 126
Therefore, the estimated number of students on the A honor roll who are 8th graders is 126.
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I need help please someone help ?
The inverses of g and h give:
g⁻¹(x) = - (x - 3)/2(g *g⁻¹)(-7) = 85h⁻¹(9) = -7How to define the inverse functions?Here we have the function:
g(x) = -2x + 3
If its inverse is g⁻¹(x), then the composition must be equal to the identity, so we can write:
g( g⁻¹(x)) = x
-2*g⁻¹(x) + 3 = x
g⁻¹(x) = (x - 3)/-2
g⁻¹(x) = - (x - 3)/2
Now we also want to get:
(g *g⁻¹)(-7)
That is the product of the two functions evaluated in -7.
(g *g⁻¹)(-7) = (-2*-7 + 3)*-(-7 - 3)/2 = 85
Now for h(x), we want to get h⁻¹(9)
By looking at the table, we can see that h(-7) = 9
Then the inverse is h⁻¹(9) = -7
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